Rogue Wave, Breathers and Bright-Dark-Rogue Solutions for the Coupled Schrödinger Equations

Guo, Boling; Ling, Liming

doi:10.1088/0256-307x/28/11/110202

Cited by 263 publications

(212 citation statements)

References 16 publications

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“…The coupled NLSE can be used to describe evolution of localized waves in a two-mode nonlinear fiber, twocomponent Bose-Einstein condensate, and other coupled nonlinear systems [18,19]. It admits the follow-ing Lax pair:…”

Section: Generalized Darboux Transformation and Rogue Wave Formulamentioning

confidence: 99%

High-order rogue wave solutions for the coupled nonlinear Schrödinger equations-II

Zhao

Guo

Ling

2016

Journal of Mathematical Physics

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We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schrödinger equations. Based on the generalized Darboux transformation and formal series method, we obtain the high-order rogue wave solution without the special limitation on the wave vectors. As an application, we exhibit the first, second-order rogue wave solution and the superposition of them by computer plotting. We find the distribution patterns for vector rogue waves are much more abundant than the ones for scalar rogue waves, and also different from the ones obtained with the constrain conditions on background fields. The results further enrich and deep our realization on rogue wave excitation dynamics in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids.

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Section: Generalized Darboux Transformation and Rogue Wave Formulamentioning

confidence: 99%

High-order rogue wave solutions for the coupled nonlinear Schrödinger equations-II

Zhao

Guo

Ling

2016

Journal of Mathematical Physics

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“…In the two-component coupled systems, dark RW was presented numerically [25] and analytically [26]. The interaction between RW and other nonlinear waves is also a hot topic of great interest [26][27][28]. For example, it has been shown that RW attracts dark-bright wave.…”

mentioning

confidence: 99%

High-order rogue waves in vector nonlinear Schrödinger equations

Ling

Guo

Zhao³

2014

Phys. Rev. E

165

122

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We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schrödinger equations. We find four fundamental rogue waves can emerge for second-order vector RW in the coupled system, in contrast to the high-order ones in single component systems. The distribution shape can be quadrilateral, triangle, and line structures through varying the proper initial excitations given by the exact analytical solutions. Moreover, six fundamental rogue wave can emerge on the distribution for second-order vector rogue wave, which is similar to the scalar third-order ones. The distribution patten for vector ones are much abundant than the ones for scalar rogue waves. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids. Introduction-Rogue wave (RW) is the name given by oceanographers to isolated large amplitude wave, which occurs more frequently then expected for normal, Gaussian distributed, statistical events [1][2][3]. It depicts a unique event that seems to appear from nowhere and disappear without a trace, and can appear in a variety of different contexts [4][5][6][7]. RW has been observed experimentally in nonlinear optics by Solli group and Kibler group [8,9], water wave tank by Chabchoub group [10], and even in plasma system by Bailung group [11]. These experimental studies suggest that the rational solutions of related dynamics equations can be used to describe these RW phenomena [12,13]. Moreover, there are many different pattern structures for high-order RW [14][15][16], which can be understood as a nonlinear superposition of fundamental RW (the first order RW). Recently, many efforts are devoted to classify the hierarchy for each order RW [17,18], since these superpositions are nontrivial and admit only a fixed number of elementary RWs in each high order solution (3 or 6 fundamental ones for the second order or third order one).

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“…MI for the VNLSE has been known for a long time [16], and its multiply periodic solutions representing the homoclinic extension of the unstable CW solutions have been obtained by methods based on the inverse scattering transform method [17][18][19][20][21][22]. These methods have been also recently applied to obtaining deterministic rogue wave (or time and space localized) solutions of the VNLSEs, which may also be coupled with bright and dark soliton solutions [23,24].…”

Section: Introductionmentioning

confidence: 99%

Even harmonic pulse train generation by cross-polarization-modulation seeded instability in optical fibers

et al. 2012

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We show that, by properly adjusting the relative state of polarization of the pump and of a weak modulation, with a frequency such that at least one of its even harmonics falls within the band of modulation instability, one obtains a fully modulated wave at the second or higher even harmonic of the initial modulation. An application of this principle to the generation of an 80 GHz optical pulse train with high extinction ratio from a 40 GHz weakly modulated pump is experimentally demonstrated using a nonzero dispersion-shifted fiber in the telecom C band.

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Rogue Wave, Breathers and Bright-Dark-Rogue Solutions for the Coupled Schrödinger Equations

Abstract: We construct explicit rogue wave solutions, breather solitons, and rogue-bright-dark solutions for the coupled non-linear Schrödinger equations by the Darboux transformation.

Cited by 263 publications

References 16 publications

High-order rogue wave solutions for the coupled nonlinear Schrödinger equations-II

High-order rogue wave solutions for the coupled nonlinear Schrödinger equations-II

High-order rogue waves in vector nonlinear Schrödinger equations

Even harmonic pulse train generation by cross-polarization-modulation seeded instability in optical fibers

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